How to adjust the edge sharpness for the subdivision surface (in edit mode)?
Use Edge Crease (&#8679; Shift+E)

Quote from the blender manual


  This edge property, a value between (0.0 to 1.0), is used by the Subdivision Surface Modifier to control the sharpness of the edges in the subdivided mesh. This operator enters an interactive mode (a bit like transform tools), where by moving the mouse (or typing a value with the keyboard) you can set the (average) crease value of selected edges. A negative value will subtract from the actual crease value, if present. To clear the crease edge property, enter a value of -1.